Meryl needs to add enough water to 11 gallons of an 18% detergent solution to make

1 answer:

8 0

The percentage here must be assumed as by volume. Therefore, it means that the solution has 0.18 gallons of detergent / gallon of solution. If Meryl needs to add 11 gallons of water then she has 2.41 gallons of detergent. Calculation is as follows:

.18 = x / x+4

Solving for x, we obtain

x = 2.41

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Q # 4 anybody help me please

Marysya12 [62]

Answer

-5/3, -1, 0.7, √2, √5

Explanation

√5 = 2.236

-1 ⇒ this is less than 1.

-5/3 = -1.666667 this is less than 1. -5/3 < -1

0.7 > -1

√2 = 1.414 ⇒ √5 > √2

Arranging them from the least to the greatest;

-5/3, -1, 0.7, √2, √5

8 0

3 years ago

Please help! A-level maths.

astra-53 [7]

$x+y=k\implies y=k-x$

Substitute this into the parabolic equation,

$k-x=6-(x-3)^2\implies x^2-7x+(k+3)=0$

We're told the line $x+y=k$ intersects $C$ twice, which means the quadratic above has two distinct real solutions. Its discriminant must then be positive, so we know

$(-7)^2-4(k+3)=49-4(k+3)>0\implies k$

We can tell from the quadratic equation that $C$ has its vertex at the point (3, 6). Also, note that

$-1\le\sin t\le1\implies3\le3+2\sin t\le5\implies3\le x\le5$

and

$-1\le\cos2t\le1\implies2\le4+2\cos2t\le6\implies2\le y\le6$

so the furthest to the right that $C$ extends is the point (5, 2). The line $x+y=k$ passes through this point for $2+5=k\implies k=7$ . For any value of $k$ , the line $x+y=k$ passes through $C$ either only once, or not at all.