0=40-10t-5t^2
t^2+2t-8=0
(t+4)(t-2)=0
t=-4 (not a solution) or t=2
Answer: after 2 seconds
(a) The measure of the indicated angle for figure 1 is 48⁰.
(b) The measure of the indicated angle for figure 2 is 42⁰.
<h3>Measure of the indicated angle</h3>
The measure of the indicated angles can be calculated as follows;
<h3>Figure 1</h3>
sinθ = opp/hypo
sinθ = 72/97
sinθ = 0.7423
θ = sin⁻¹(0.7423)
θ = 47.9⁰ ≈ 48⁰
<h3>Figure 2</h3>
sinθ = 65/97
sinθ = 0.6701
θ = sin⁻¹(0.6701)
θ = 42.1⁰ ≈ 42⁰
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Answer:
she can make 6 baskets with the bars of lavender soap 4 baskets with the bottles of shampoo and 7 baskets with the tubes of hand lotion
Step-by-step explanation:
Angle AOD and < BOD are supplementary since they are both right angles which equal 180°.
<h3>What is a supplementary angle?</h3>
It should be noted that a supplementary angle simply means an angle that adds up to 180°.
In this case, the angles given are both rights angles. This will be:
= 90° + 90°
= 180°
In this case, Angle AOD and < BOD are supplementary since they are both rights angles which equal 180°.
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Lets solve the problem through compound interest formula,
The number of months are 360
The account pay interest rate is 5.1 %compounded monthly.
The amount withdraws each month is $2154
The value of n is 360.
The value of is<em> i</em> is 5.1%
So,
![P = A [(1+i)^n]-1/i(1+i)^n\\\\P = $2,154 [(1+(0.051/12))^30*12] - 1 / (0.051/12)(1+(0.051/12))^30*12\\\\P = $396,721.78](https://tex.z-dn.net/?f=P%20%3D%20A%20%5B%281%2Bi%29%5En%5D-1%2Fi%281%2Bi%29%5En%5C%5C%5C%5CP%20%3D%20%242%2C154%20%5B%281%2B%280.051%2F12%29%29%5E30%2A12%5D%20-%201%20%2F%20%280.051%2F12%29%281%2B%280.051%2F12%29%29%5E30%2A12%5C%5C%5C%5CP%20%3D%20%24396%2C721.78)
Hence the value of principal is $396721.78
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