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3 years ago

I need help solving 10e^3t = 60

Mathematics

1 answer:

Fofino [41]3 years ago

4 0

Step-by-step explanation:

10e³ᵗ = 60

e³ᵗ = 6

3t = ln 6

t = ⅓ ln 6

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The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second.

pickupchik [31]

Answer: first option.

Step-by-step explanation:

The ratio of the area of the triangles can be calculated as following:

$ratio_{(area)}=(\frac{l_1}{l_2})^2$

Where $l_1$ is the lenght of the given side of the smaller triangle and $l_2$ is the lenght of the given side of the larger triangle.

Therefore:

$ratio_{(area)}=(\frac{28}{32})^2=\frac{49}{64}$

It can be written as following:

$ratio_{(area)}=49:64$

The ratio of the perimeter is:

$ratio_{(perimeter)}=\frac{l_1}{l_2}$

Where $l_1$ is the lenght of the given side of the smaller triangle and $l_2$ is the lenght of the given side of the larger triangle.

Therefore:

$ratio_{(perimeter)}=\frac{28}{32}=\frac{7}{8}$

It can be written as following:

$ratio_{(perimeter)}=7:8$

5 0

2 years ago

A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep

prohojiy [21]

The sketch of the parabola is attached below

We have the focus $(a,b) = (2, -0.5)$
The point $P(x,y)$
The directrix, c at $y=-1.5$

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; $(2, -0.5)$ and $(x,y)$ .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$

Step 2
Find the distance between the point P to the directrix $c$ . It is a vertical distance between y and c, expressed as $y-c$

Step 3
The equation of parabola is then given as
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$ = $y-c$
$(x-a)^{2}+ (y-b)^{2}= (y-c)^{2}$ ⇒ substituting a, b and c
$(x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2}$
$(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}$ ⇒Rearranging and making $y$ the subject gives

$y= \frac{ x^{2} }{2} -2x+1$

7 0

3 years ago

HELP WITH PROBABILITY! WILL MARK BRAINLIEST!!

IRISSAK [1]

Answer:

4th and 3rd of August and then we will have a WONDERFUL Heathers day trip and I am going back home for the weekend of you and the kids

3 0

2 years ago

PLEASE! PLEASE! help!

qaws [65]

1.) The answer is 825.75 (multiply the given tax rates to the gross pay)
2,785 x 13% federal taxes = 362.05
2,785 x 9% state tax = 250.65
2,785 x 7.65% FICA = 213.05
 825.75

2.) The answer is 288.60 (multiply the interest rate to the balance, no need to add a late payment fee since they paid on 6/1, not after)
2,748.56 x 10.5% = 288.60

3.) The answer is 182.13 (multiply the APR to the original purchase price, no need to add the sales tax)
 1,500 x 11.75% = 182.13

4.) The answer is 371.92 (deduct the reward to the interest)
Interest : 2,975.34 x 13.5% = 401.67
Reward : 2,975.34 x 1% = 29.75
371.92

5.) The answer is 1,339.13 (deduct the interest to the monthly payment)
Monthly payment : 2,236.00
Monthly interest : 896.87 [(231,450 x 4.65%) / 12 months]
 1,339.13

Hope this helps! :)

4 0

2 years ago

How many eighths in one half

11111nata11111 [884]

4/8 = 1/2 so it is four eigths in one half. 4/8 simplified is 1/2

4 0

2 years ago

Read 2 more answers